Preheat oven to 350°F (175°C). Grease and flour an 8x8-inch pan.
Whisk flour, baking powder, salt, cinnamon, and nutmeg in a medium bowl.
In a large bowl, mix melted butter and brown sugar until smooth. Add eggs and vanilla, beating until combined.
Gradually stir dry ingredients into wet until just incorporated. Don’t overmix.
Fold in chopped apples gently.
Spread batter into prepared pan and bake 30–35 minutes, or until a toothpick inserted in the center comes out clean.
While brownies cool, whisk powdered sugar, maple syrup, and milk until smooth, adjusting milk for thickness.
Drizzle glaze over cooled brownies, slice, and serve.